An    Lxperiment  To    Determine 
The  Number  of  Repetitions 

Necessary  to  Memorize  and  Retain 
With  Maximum  Certainty 

A  Miscellaneous  Collection  of  Facts 


A  THESIS  presented  to  the  Faculty  of  the  Graduate  School 

Of   the   UNIVERSITY    of    PENNSYLVANIA 

In  Part  Fulfilment  of  the  Requirements  for  the 

Degree  of  Doctor  of  Philosophy 


BY 


A.  L.  WAGNLR,  Ph.  D. 


Nesquehoning,  Pa. 

MAY     1910 


The  Number  of  Repetitions  Necessary  to  Memorize 

And  Retain  With  Maximum  Certainty 

A  Miscellaneous  Collection  of  Facts 

INTRODUCTION 

The  Jesuit  Schools  for  more  than  a  century  were 
the  unrivaled  leaders  in  the  educational  world.  Their 
aim  was  to  prepare  for  leadership  in  the  evangelization 
f)f  humanity.  Their  entire  system  was  based  upon  the 
l>rinciple  that  it  is  better  to  teach  a  relatively  small 
amount  in  a  thorough  manner,  than  to  give  an  in- 
definite impression  of  a  much  larger  quantity.  They 
gave  freciuent  reviews,  Kach  day  began  with  a  review 
of  the  things  taught  on  the  previous  day;  each  week 
ended  with  a  review  of  the  things  presented  during  this 
time;  each  year  was  closed  with  a  review  of  the  work 
done  that  year;  and  the  whole  course  was  then  reviewed 
by  teaching  it.  The  entire  s^^stem  had  as  one  of  its 
leading  characteristics  frequency  of  repetition  accom- 
panied by  prelection  and  erudition.  The^^  succeeded  in 
securing  intellectual  development  and  the  results  de- 
sired were  always  certain. 

After  the  Jesuits,  Ratick  was  the  first  to  realize 
that  educational  method  must  secure  maximum  cer- 
tainty of  recall,  and  that  this  is  obtained  best  by 
repetition.  One  thing  at  a  time  and  that  often  repeated 
was  one  of  his  maxims.  He  had  the  sagacity  to  foresee 
that  successful  mastery  necessitated  a  relatively  small 
content,  though  he  failed  to  construe  "one  thing"  as  a 
basal  element  in  thinking,  a  point  or  unit  of  subject 
matter,  and  ofte(i  repeated  and  re-repeated  his  *'one 
thing"  until  some  things  were  repeated  to  death.  He 
was  not  sagacious  enough,  however,  to  perceive  the 
wisdom  of  using  the  children  of  his  school  to  determine 
the  conditions  under  which  repetition  will  most  advan- 
tageoush'  secure  maximum  certainty  of  recall. 

251388 


^.,  ...OThe  i|e^t 'attempt  that  was  made  along-  the  lines  of 

^.t?t?pe€ition  .*to  'secure  mastery   was   made    by    Professor 

Cornman  of  Columbia  in  connection  with  the  spellinjr. 

In  the  investigation  hereinafter  described,    an   attempt 

is  made  to  secure  information  along  the  same  lines. 

Practical  pedagogy  makes  it  necessary  that  we 
know  more  definitely  how  to  secure  the  excellences  of 
the  method  of  repetition  used  by  the  Jesuits  and  Katick 
and  how  to  avoid  its  defects.  This  knowledge  can  not 
be  gleaned  by  the  application  of  theoretical  psychology 
but  must  be  derived  from  facts  scientifically  determined. 

That  scientific  methods  should  be  used  in  procur- 
ing pedagogical  knowledge  or  in  deriving  facts  upon 
which  principles  may  be  formulated,  may  seem  strange, 
but  it  is  in  no  w^a.y  more  unusual  than  the  use  of  the 
same  methods  in  any  other  field  of  human  endeavor. 
The  good  teaching  which  we  have  will  be  improved  as 
soon  as  principles  based  upon  facts  scientifically  deter- 
mined are  applied  in  the  practical  work  of  the  school 
room.  Valuable  indeed  to  any  teacher  will  it  be  to  know 
the  number  of  repetitions  needed  by  children,  under 
ordinary  circumstances,  to  learn  things,  and  equally 
valuable  -will  it  be  to  know  how^  frequent  the  repetitions 
must  be  in  order  that  the  facts  may  be  retained  when 
once  they  are  learned. 

In  the  experiments  of  which  a  description  follows, 
an  attempt  was  made  to  determine: 

1.  How  many  repetitions  are  necessary  to  secure 
the  mastery  of  facts  with  maximum  certainty;  and 

2.  At  Avhat  intervals  the  repetitions  must  occur 
in  order  that  the  mastery,  when  once  secured, 
ma3^  be  retained. 


3 
THE  FIRST  EXPERIMENT. 

When  the  experiment  was  first  begun,  it  seemed  reason- 
ably certain  to  the  experimenter  that  the  written  form  of  repe- 
tition would  be  the  most  desirable.  Questions,  the  answer 
to  which  could  be  e^iven  in  a  single  sentence,  or  even  a  single 
word,  were  selected  and  given  in  order  to  avoid  the  element 
of  judgment  in  determining  the  relative  worth  of  the  answers, 
and  in  order  to  insure,  with  maximum  certainty,  that  the 
answers  given  would  be  either  entirely  correct  or  incorrect. 
Instead,  however,  of  giving  the  single  word  desired  as  the 
answer  to  the  question,  a  number  of  the  children  substituted 
other  terms  from  which  it  was  impossible  to  determine  whether 
they  retained  the  major  portion  of  the  original  presentation ; 
or  whether,  as  the  word  used  in  answering  often  indicated, 
they  retained  but  a  small  portion  of  the  content  of  the  word 
desired  for  an  answer  which  the  original  presentation  was 
intended  to  give.  In  a  number  of  instances,  the  words  which 
were  used  in  answering  the  question  may  have  or  may  not 
have  signified  that  the  original  presentation  was  retained.  In 
writing  the  names  of  two  rivers  of  Africa  as  the  "Murray  of 
Darling"  instead  of  the  Murray  and  Darling,  unless  one  is  will- 
ing to  assume  that  the  placing  of  the  "of"  instead  of  the  "and" 
was  a  mere  slip  of  the  pencil,  the  conclusion  that  much  of 
the  original  presentation  was  no  longer  functioning  is  inevi- 
table. A  similar  illustration  occurred  with  the  words  "llanos," 
"lepidodendron,"  "Locust  Mt."  and  others.  Were  I  to  try 
the  experiment  again,  other  forms  of  writing  the  answer  than 
writing  merely  one  word  would  be  used. 

The  presentation  of  the  facts  in  each  case  was  as  clear 
and  as  full  as  the  presenter  could  make  it.  All  forms  of  pres- 
entation were  used  that  could  be  thought  of.  The  facts  to  be 
remembered  were  illustrated  by  pictures,  stories,  and  drawings. 
Every  form  of  apperceptional  contribution  known  to  be  avail- 
able was  utilized. 

Some  of  the  repetitions  were  called  for  by  the  teacher, 
others  by  the  experimenter.  That  the  number  of  errors  is  as 
small  as  it  is,  may  be  due  to  the  fact  that  the  desire  on  the 
part  of  the  teacher  to  have  her  room  make  a  good  showing  was 
stronger  than  her  desire  to  have  the  experiment  scientifically 
accurate.  ' 

Only  such  facts  were  presented  as  seemed  to  be  unknown 
to  the  children  with  whom  the  experiment  was  tried.  Some 
of  these  were  selected  because  of  their  local  significance,  and 
because  it  was  somewhat  difficult  to  find  facts  with  which  chil- 
dren of  an  entire  group  who  had  completed  an  elementary 
geography  and  history  were  unfamiliar.  This  is  especially  true 
of  the  facts  that  were  used  with  the  seventh  and  eighth  grades. 

All  facts  were  presented  at  one  sitting  by  myself.  This 
required   three-fourths  of   an   hour   for  the   fifth,   sixth,   and 


4 

eighth  grade,  and  one  and  one- fourth  hours  for  the  seventh 
grade.  When  the  fact  had  been  presented  by  the  experi- 
menter, the  answer  desired  for  future  repetitions  was  written 
upon  the  blackboard  by  himself,  and  upon  a  slip  of  paper  by 
the  children.  When  all  the  facts  had  been  presented  these 
papers  were  collected.  At  each  repetition  the  questions  were 
asked  by  the  experimenter  or  the  teacher,  and  the  answers  were 
written  upon  slips  of  paper  by  the  children  in  the  same  manner 
as  spelling  words  are  usually  written.  The  errors  were  then 
marked  by  the  children,  each  retaining  his  or  her  own  slip,  the 
experimenter  or  the  teacher  repeating  the  correct  answers  in 
their  numerical  order.  Each  child  making  an  error  was  re- 
quired to  write  the  correct  answer  at  the  close  of  the  exercise. 
Before  the  papers  containing  the  children's  answers  were  filed 
and  before  the  exercise  was  over  all  papers  were  looked  over 
by  the  experimenter  or  the  teacher  to  avoid  having  mistakes 
pass  unnoticed.  The  number  of  repetitions  as  indicated  on  the 
sheets  containing  the  results  means  the  number  of  times 
that  they  were  written  on  paper,  except  in  the  eighth  grade 
where  they  were  repeated  orally. 

The  papers  containing  the  results  of  the  first  repetitions 
showed  a  lamentable  lack  on  the  part  of  the  slow  learners  to 
get  the  correct  spelling  of  the  terms  required  in  the  answers. 
No  attempt  was  made  to  secure  correct  spelling  by  having  a 
repetition  of  the  fact.  In  giving  the  correct  answer  while  the 
errors  were  being  marked  the  teacher  or  the  experimenter 
spelled  the  word  instead  of  saying  it.  It  is  possible  that  this 
form  of  oral  repetition  aided  in  impressing  the  fact  to  be  re- 
membered as  well  as  the  spelling  of  the  word  that  stood  for 
it.  It  was  necessary  to  spell  the  answers  five  times  with  the 
sixth  grade  folks  in  order  to  secure  maximum  correctness  of 
s])elling,  while  with  the  seventh  it  required  but  three,  and  with 
the  fifth  two. 

The  questions  which  were  given  to  the  fifth  grade  with 
the  answers  that  were  desired  follow : 

1.  What  important  geographical  circle  crosses  South  America 

near  the  mouth  of  the  Amazon  River?    The  Equator. 

2.  What  important  geographical  circle  crosses  South  America 

near  the  location  of  the  city  of  Rio  Janeiro?     The 

Tropic  of  Capricorn. 
What  season    do    they    now    have    a  t  Buenos    Ayres  ? 

Autumn. 
What  ocean  borders  the  eastern  side  of  South  America? 

The  Atlantic. 

5.  What  island  at  the  southern  extremity  of  South  America? 

Terra  del  Fuego. 

6.  What  cape  at  the  southern  extremity  of  this  island?  Cape 

Horn. 
What  is  the  largest  river  of  South  America?    Amazon. 


o 

8.  What  strait  between  Terra  del  Fiiego  and  South  America? 

Strait  of  Magellan. 

9.  What  is  the  island  at  the  mouth  of  the  Orinoco  River 

and  for  what  is  it  noted?    Trinidad,  noted  for  pitch. 

10.  What   mountains   along-    the    western    coast    of    South 

America  ?     Andes. 

11.  How   are  the  summits   during  the   entire  year?     Snow 

covered. 

12.  What  three  important  minerals  are  found  in  these  moun- 

tains?    Gold,  silver  and  copper. 

13.  What  three  animals  inhabit  the  Andes  regions?    Condor, 

llama  and  alpaca. 

14.  Name  two  highland  regions  of  South  America.     Andes 

and   Brazilian. 

15.  Where  is  the  rainiest  region  of  the  world?     Along  the 

Amazon. 

16.  Name  three  valuable  trees  that  grow  in  South  America 

Mahogany,  rosewood  and  india-rubber. 

17.  What  is  the  name  given  to  the  plains  along  the  Orinoco 

River  ?     Llanos. 

18.  What  two  seasons  do  they  have  in  Venezuela?  The  Rainy 

and  the  Dry. 

19.  What  name  is  given  to  the  plains  along  the  Amazon? 

Silvas. 

20.  About  how  many  miles   from  the  most  northern  to  the 

most  southern  point  of  South  America?    About  1500. 

A  glance  at  the  questions  will  show  that  they  all  refer 
to  South  America  and  that  there  is  nothing  like  a  logical  order 
in  their  arrangement.  The  answers  desired  to  three  of  them 
require  three  words,  similar  in  the  sense  that  three  of  these 
are  mineral  products,  three  are  the  names  of  animals,  and  the 
three  remaining  ones  the  names  of  trees.  The  effect  of  this 
association  will  be  noted  in  the  results. 

The  questions  with  the  answers  that  were  desired  which 
follow  are  the  ones  that  were  given  to  the  sixth  grade: 

1.  About  how  large  is  Australia?     About  as  large  as  the 

United  States,  about  31-2  million  square  miles. 

2.  How  is  the  interior  portion  of  the  Australian  continent 

with  respect  to  heat  and  moisture?     It  is  a  desert. 

3.  What  valuable  mineral  is  extensively  mined  in  Australia? 

Gold. 

4.  What  is  the   leading  occupation  in   New  South  Wales? 

.   Stock  raising. 

5.  Sydney  has   an   extensive   trade   with   wKat   city   in  the 

United  States?     San  Francisco. 

6.  To  what  race  do  the  native  tribes  belong?     Hamitic  or 

Black  Race. 

7.  Name  three  important  trees  of  Australia.     Bread-fruit, 

cocoa-palm  and  banana. 


6 

8.  What  is  exported  from  South  Australia?     Wool,  grain 

and  copper. 

9.  What  is  the  religion  of  the  native  tribes?     Cannibalism. 

10.  Name  two  of  the  most  noted  cities.    Melbourne  and  Syd- 

ney. 

11.  How  are  the  Australian  colonies  united?     Into  the  com- 

monwealth of  Australia. 

12.  About  what  is  the  latitude  of  Melbourne?    About  40  de- 

grees South  latitude. 
13..     What  three  valuable  fruit  trees  grow  in  Australia?     Ba- 
nana, bread-fruit  and  cocoa-palm. 

14.  By  what  kind  of  people  was  Australia  colonized  ?   English 

convicts. 

15.  When  was  the    Australian    Commonwealth     established? 

Jan.   1,   1901. 

16.  W^hat  are  the  two  most  important  rivers  of  Australia? 

Murray  and  Darling. 

17.  How   far  from  Australia  are    the   Fiji   Islands?     1200 

miles  east. 

18.  What    island    near    the    southern   coast   of   Australia   is 

covered  with  dense  forests?    Tasmania. 

19.  In  what  city  of  Australia  did  the  lady  live  who  recently 

visited  our  school?     Ballarat. 

20.  What  is  the  principal  animal  native  to  Australia?     The 

kangaroo. 
The  questions  that  were  used  with  the  seventh  grade  were 
those  that  follow : 

About   what   is  the  area  of   Mauch   Chunk   Township? 

Twenty  square  miles. 
At  the  base  of  what  mountain  is  this  school  building? 

Sharp. 
What  mountain  on  the  opposite  side  of  Panther  Creek 

Valley  ?     Locust. 
How  high  above  the  sea  level  is  the  Lehigh  River  at  Le- 
high Gap.     389  feet. 
About  how  high  above  the  sea  level  is  Mt.  Pisgah?    1340 

feet. 
6.     What  is  the  meaning  of  Nesquehoning?    Narrow  Valley. 
7.      At  what  i>lace  was  Carbon  County  first  settled?    At 

Gnaden  Hutten. 
Write  the  name  of  the  religious  sect  and  the  leader  of 

those  who  made  the    first    settlement.      Moravians, 

Zinzendorf. 
Indians  from  what  two  tribes  did  the  Moravians  try  to 

convert  to  Christianity?     Delawares  and   Mohicans. 
10.     What  was  the  name  of  the  family  that  the  Indians  carried 

into  captivity?    Gilbert  Family. 
IT.     What  relic  of  this  captivity  is  still  to  be  seen  in  Mauch 

Chunk?     A  Moccasin. 


7 

12.  Where  was  the  first  white  man's  home  built  in  Mauch 

Chunk  Township?     Lausanne. 

13.  The  boyhood  of  what   famous  artist  was  spent  at  this 

place  ?     Rothermel. 

14.  To  what  man  of  Washington's  army  did  Lydia  Darrh 

give  the  information  that  the  British  generals  had 
planned  an  attack  on  the  Americans  in  her  house? 
Colonel  Craig  of  Carbon  County. 

15.  Who  is  the  most  influential  man  connected  with  the  his- 

tory of  Carbon  County?    Asa  Packer. 

16.  What  important  rock  strata  have  their  outcrop  at  Mauch 

Chunk?     Mauch  Chunk  Red  Shale. 

17.  What  layer  of  rock  strata  forms  the  top  and  the  bottom 

of  the  coal  measures?     Pottsville  Conglomerate. 

18.  What  is  the  thickness  of  the  coal  measures?     1855  feet 

19.  What  is  the  name  of  the  plant  that  formed  the  larger  part 

of  these  coal  strata?    Lepidodendron. 

20.  What  is  coal?     Locked  up   sunlight. 

It  will  be  observed  that  the  questions  for  this  group  are 
questions  that  deal  with  facts  that  have  only  local  value,  and 
that  all  of  them  were  extremely  valuable  and  significant  to 
the  group  of  children  to  whom  they  were  given.  Not  one  of 
the  group  had  previously  had  any  idea  as  to  the  area  of  the 
township  in  which  they  lived.  Questions  i  and  2  referred  to 
the  two  mountains  which  enclosed  the  valley  in  which  the 
children  lived.  The  names  presented  are  those  that  were 
applied  by  the  Pennsylvania  Geological  Survey.  A  number 
of  the  children  of  the  group  had  names  for  these  mountains 
that  they  had  gotten  by  tradition  but  the  names  were  as  various 
as  they  were  numerous.  The  effect  of  this  learning  another 
name  for  the  same  thing  was  not  noted  as  carefully  as  it 
should  have  been,  but  the  answers  to  these  two  questions  at 
least  were  not  different  enough  from  the  others  to  make  them 
especially   noticeable. 

Not  any  of  the  children  had  any  idea  of  the  height  of  the 
mountains  in  the  midst  of  which  they  lived.  In  the  presenta- 
tion of  questions  4  and  5  the  height  of  a  number  of  the  moun- 
tnins  in  the  county  was  told  to  the  children  but  only  the 
highest  and  the  lowest  point  was  required.  The  remember- 
ing of  these  numbers  presented  no  unusual  difficulty,  and  the 
time  of  forgetting  was  too  short  to  really  determine,  though 
it  is  ])Ossible  that  the  names  would  stick  longer  than  the  figures 

Questions  7  and  to  refer  to  Indian  massacres  and  raias 
that  were  made  on  the  inhabitants  of  the  region  after  the 
defeat  of  Braddock.  The  stories  of  these  massacres  with 
tlieir  ethical  significance  was  g-iven  during  their  presentation. 
The  same  is  true  of  8,  9  and  it. 

The  story  referred  to  in  14  was  new  to  nearly  all  of  the 
children,  and  Colonel  Craig's  connection  with  it  they  had  never 


8 
known,  though  a  number  of  them  knew  many  of  the  Craig 
descendants. 

With  number  15  was  presented  the  navigation  of  the  Le- 
high, the  building  of  the  Lehigh  Valley  Railroad  and  the  found- 
ing of  Lehigh  University. 

The  geological  strata  referred  to  in  the  remaining  ques- 
tions were  explained  and  illustrated  by  drawings  and  examples, 
and  attention  was  called  to  a  collection  of  strata  near  trie  school 
building  where  the  rocks  which  were  once  flat  have  been 
tilted  into  an  almost  vertical  position  and  attain  to  an  altitude 
of  over  1400  feet.  This  illustrating  and  explaining  was  es- 
pecially true  of  questions  19  and  20. 

The  questions  used  with  the  eighth  grade  were  given 
about  the  time  the  group  was  having  its  final  review  in  geog- 
raphy. It  was,  therefore,  somewhat  difficult  to  select  geo- 
graphical questions  with  which  the  entire  group  was  entirely 
unfamiliar.  The  questions  that  follow  are  the  ones  that  were 
used: 

1.  What  is  proved  by  the  shadow  which  the  earth  casts  on 

the  moon?    That  the  earth  is  round. 

2,  Name  the  three  planets    nearest    the    earth.      Mercury, 

Venus,   Mars. 

3.  What  keeps  bodies  on  the  surface  of  the  earth  ?    Gravity. 

4.  What  changes  are  caused  by  the  revolution  of  the  earth 

around  the  sun?     Change  of  seasons. 

5.  What  instrument  do  mariners  use  to  determine  direction? 

Compass. 

6.  Latitude  is  measured  on  what  lines?     Meridians. 

7.  The  great  highlands  of  the  continents  form  a  great  horse- 

shoe  from   where   to   where?     Cape  Horn   to  Good 
Hope. 

8.  Which  planet  has  four  moons?     Jupiter. 

9.  Which  planet  has  the  rings?     Saturn. 

10.  How  have  mountains  been  formed?     By  the  folding  of 

the  rock  layer. 

11.  What  term  is  applied  to  the  wearing  away  of  the  land? 

Erosion. 

12.  Give  the  most  noted    example    of     erosion     in     Carbon 

County.     Lehigh  Gap. 

13.  What  is  the  inclination  of  the  earth's  axis?     23  1-2  de- 

grees. 

14.  If  the  earth  inclined  33  1-2  degrees  what  would  the  width 

of  the  temperate  zone  be  ?    23  degrees. 

15.  What  is  the  name  of  the  path  in  which  the  earth  travels 

around  the  sun?     Orbit. 

16.  The  Frigid  Zone  is  cold  because  the  sun's  rays  fall  how? 

Slanting. 

17.  What  is  wind  and  how  caused?     Air  in  motion  caused 

by  its  unequal  heating. 


9 

i8.     What   usually   causes  deserts?       Mountains  or   lack  of 
them. 

19.  Give  the  scientific  name  for  the  black  race.    Ethiopian. 

20.  What  prevents  the  possibility  of  boiling  eggs  on  the  sum- 

mits of  the  highest  mountains?     Atmospheric  pres- 
sure. 

21.  What  barrier  causes  the  fauna  of  Australia  to  differ  from 

the  rest  of  the  world?     The  ocean. 

W^ith  the  eighth  grade  each  repetition  was  conducted  orally 
during  the  various  parts  of  the  day  indicated.  This  would 
give  the  individuals  that  were  not  reciting  an  opportunity  to 
hear  17  repetitions;  since,  however,  individuals  were  called 
upon  at  irregular  periods  of  the  day  such  as  suited  the  con- 
venience of  the  teacher  or  pupil,  it  is  probable  the  attention 
of  each  pupil  was  concentrated  on  some  personal  and  individ- 
ual task,  and  that  not  nearly  seventeen  repetitions  were  heard 
by  any  one  pupil. 

In  conducting  this  experiment  such  disposal  of  the  diffi- 
culties that  presented  themselves  was  made  as  the  exigencies  of 
the  case  seemed  to  warrant.  The  results  are  reliable  only 
to  the  extent  of  being  reasonably  approximate.  Among  the 
factors  which  prevented  the  experiment  from  being  scientifi- 
cally accurate  are  the  following: 

1.  The  number  of  individuals  with  whom  the  experi- 
ment was  tried  was  too  small.  The  experiment  should  be 
tried  with  a  large  number  of  pupils,  several  thousand. 

2.  The  number  of  slow  learners  varied  in  several  of  the 
groups  and  would  proportionately  modify  the  showing  of  the 
group. 

3.  The  period  during  which  the  experiment  was  con- 
ducted was  entirely  too  short  to  conclude  that  the  facts  pre- 
sented and  repeated  were  fixed  with  maximum  certainty  of 
permanent  recall.  It  took  but  a  very  short  time  until  the  facts 
were  fixed,  but  the  term's  close  was  too  near  to  allow  the 
interval  between  the  various  repetitions  to  be  constantly  in- 
creased. 

4.  The  number  of  repetitions  was  modified  by  some  of 
the  children  using  them  after  the  fourth  repetition  in  their 
playing  school.  The  brighter  children  of  the  fifth  grade 
could  repeat  the  questions  and  answers  after  the  fourth  repe- 
tition, and  used  them  in  the  hall  as  lesson  for  their  play  school. 
Individuals  of  the  other  grades  also  were  observed  to  ask 
the  questions  at  random  of  each  other. 

5.  The  facts  should  always  be  presented  by  the  same 
individual  so  there  could  be  associated  with  each  individual 
fact  the  same  bits  of  interesting  detail  that  would  make  all 
the  facts  equally  well  remembered  by  each  group  of  children 
and  each  fact  equally  as  fully  apperceived. 

6.  The  desire  and  anxiety  on  the  part  of  some  of  the 


10 

teachers  whose  children  were  experimented  upon  to  have  the 
results  appear  well  may  have  caused  them  to  give  hints  during 
the  repetitions  that  slightly  modified  the  results. 

7.  In  several  cases  the  word  required  for  the  answer 
was  correctly  retained,  but  the  content  which  the  presenter 
had  hoped  to  connect  with  it  permanently  could  not  be  even 
reproduced  in  part,  and  was  probably  entirely  forgotten. 

8.  Answers  were  received  that  were  substitutes  for  the 
ones  required,  and  from  these  answers  it  was  impossible  to 
determine  whether  the  child  had  the  presentation  that  was 
given,  or  whether  apperception  had  made  such  contributions 
and  association  had  caused  such  related  ideas  to  function  that 
the  content  in  the  learner's  mind  no  longer  corresponded  to 
that  at  the  close  of  the  original  presentation. 

In  an  examinaion  of  the  fifth  and  sixth  year  folks  that 
was  given  at  the  end  of  the  school  year,  in  answer  to  the  gen- 
eral question,  "Tell  all  you  can  of  South  America,"  **of  Aus- 
tralia;" each  individual  included  in  his  answer  some  of  the 
facts  that  were  presented  in  the  experiment.  One  individual, 
a  fifth  grade  pupil,  included  eighty-one  per  cent.,  and  no  in- 
dividual had  less  than  twenty  per  cent. 

The  question  relating  to  the  formation  of  the  Australian 
Federation,  the  date  1908  was  substituted  for  the  one  re- 
quired by  two  individuals  on  three  different  repetitions. 

In  the  case  of  questions  that  were  so  framed  as  to  re- 
quire two  or  more  words  for  an  answer,  during  the  earlier 
repetitions,  it. happened  that  only  part  of  the  required  answer 
was  recallable ;  this  same  thing  did  not  occur  during  the  later 
repetitions,  due  possibly  to  the  fact  that  the  associations  be- 
tween the  various  parts  of  the  answer  became  more  perma- 
nent as  the  result  of  the  oral  repetitions  of  the  errors  that 
were  made  during  the  written  repetition. 

By  an  examination  of  the  sheets  containing  the  results  it 
will  be  seen  that  the  fifth  grade  folks  practically  knew  the 
twenty  questions  at  the  end  of  the  fourth  repetition,  the  sixth 
year  folks  by  the  end  of  the  fifth  repetition,  the  seventh  year 
folks  by  the  end  of  the  fourth  repetition,  and  the  eighth 
year  folks  by  the  end  of  the  third  repetition.  Averaging  these 
approximations  the  statement  might  be  made  that  the  twenty 
facts  were  learned  with  four  repetitions. 

That  the  outcome  of  the  experiment  should  be  as  it  is, 
surprises  no  one  more  than  myself.  Though  these  results 
lack  absolute  exactness,  they  are  sufficiently  exact  to  give 
us  the  information  necessary  to  direct  intelligently  our  future 
educational  method,  and  aid  us  in  the  intelligent  selection  of 
our  education  content.  It  is  accurate  in  a  sufficient  degree 
to  indicate  to  us  the  kind  of  method  that  should  be  used 
to  fix  essential  content.  The  essential  feature  of  this  method 
must  be.   not   several   repetitions  in   a  short  period  of  time; 


11 

but  a  relatively  small  number  of  repetitions  with  a  constantly 
increasing  interval  of  time  l>etween  the  repetitions  that  con- 
tinue through  rather  a  long  period. 

In  the  results  which  follow,  the  numbers  along  the  left 
hand  sic'e  of  the  column  of  figures  indicate  the  number  of 
pupils.  Absences  are  indicated  with  a  cross.  The  numbers 
below  the  repetitions,  as  indicated  at  the  top  of  the  columns, 
denote  the  number  of  errors  that  were  made  by  the  various 
individuals.  The  date  at  the  top  of  each  column  means  that 
the  repetition  was  conducted  upon  that  day. 


12 
Results  with  Fifth  Grade 


^       ^  r.        -        ^       2       ^ 


C3 

TO 

S 

< 

0. 

< 

< 

^ 

.^ 

^ 

6 
Z 

y> 

'a. 

3 

1 

d. 

0. 

0) 

D 

ex 

>< 
(7) 

d. 

> 

tuO 

d. 

d. 

a: 

I 

5 

3 

0 

0 

0 

0 

0 

0 

0 

0 

2 

3 

3 

2 

1 

0 

I 

0 

0 

0 

0 

3 

5 

2 

I 

0 

0 

0 

0 

0 

0 

0 

4 

2 

0 

0 

I 

0 

0 

0 

0 

0 

0 

5 

6 

4 

3 

2 

0 

0 

I 

0 

0 

0 

6 

7 

2 

5 

3 

I 

0 

0 

0 

0 

0 

7 

8 

4 

3 

0 

0 

2 

I 

0 

0 

0 

8 

4 

I 

2 

0 

I 

0 

0 

0 

I 

0 

9 

5 

3 

0 

0 

0 

0 

0 

0 

0 

0 

lO 

3 

2 

0 

0 

0 

0 

0 

0 

0 

0 

11 

5 

3 

0 

I 

0 

0 

I 

0 

0 

0 

12 

3 

5 

2 

1-3 

0 

0 

0 

0 

0 

0 

13 

6 

2 

0 

0 

1-3 

0 

0 

0 

0 

0 

14 

3 

2 

0 

0 

0 

0 

0 

0 

0 

0 

15 

5 

4 

0 

I 

0 

0 

1-3 

0 

0 

0 

i6 

I 

0 

0 

0 

0 

0 

0 

0 

0 

0 

17 

4 

2 

0 

1 

0 

0 

0 

0 

0 

0 

i8 

7 

4 

2 

2 

0 

I 

0 

0 

0 

19 

2 

0 

0 

I 

0 

0 

0 

0 

0 

0 

20 

4 

3 

2 

I 

0 

I 

0 

0 

I 

0 

21 

6 

2 

0 

0 

0 

0 

0 

0 

0 

0 

22 

5 

2 

I 

I 

0 

0 

0 

0 

0 

23 

3 

0 

0 

0 

0 

0 

0 

0 

0 

0 

24 

5 

4 

I 

0 

0 

0 

0 

1 

0 

0 

25 

6 

I 

0 

0 

0 

I 

0 

0 

2-3 

0 

26 

7 

2 

0 

0 

1-3 

0 

0 

0 

0 

0 

27 

4 

4 

4 

3 

I 

0 

0 

I 

0 

0 

28 

9 

7 

6 

4 

2 

0 

2 

I 

0 

0 

29 

7 

5 

3 

0 

I 

0 

0 

0 

0 

0 

30 

61 

-3  3 

0 

I 

0 

0 

0 

0 

0 

0 

31 

14 

12 

7 

4 

3 

0 

0 

0 

0 

32 

7 

4 

2 

0 

5 

I 

0 

0 

0 

I 

33 

6 

3 

0 

0 

0 

0 

0 

0 

0 

0 

34 

12 

4 

3 

0 

0 

2 

0 

I 

0 

0 

35 

3 

4 

2 

I 

0 

I 

0 

0 

0 

0 

36 

7 

2 

2 

0 

I 

0 

0 

0 

I 

0 

37 

6 

41 

-30 

2 

0 

0 

0 

0 

0 

0 

38 

I 

0 

0 

0 

0 

0 

0 

0 

0 

0 

39 

3 

0 

I 

0 

0 

0 

0 

0 

0 

0 

40 

I 

0 

0 

I 

0 

0 

0 

0 

0 

0 

13 
Results  with  Sixth  Grade 


d 

in 

CO 

6. 

ft: 

1 

0 

ro 

a: 

< 

d. 

rg 
0. 

< 

d. 

& 

u. 

a. 
< 

du 

X 

0 

ro 

«-I 

0. 
< 

d. 
<u 

> 

<u 

CO 

d, 

UJ 

d. 

c 
Z 

CS 

d. 

I 

4 

3 

2 

I 

0 

0 

0 

0 

0 

0 

2 

3 

4 

0 

I 

I 

I 

0 

0 

0 

0 

3 

3 

I 

0 

3 

3 

2 

0 

0 

0 

0 

4 

7 

5 

0 

4 

2 

0 

0 

I 

0 

0 

5 

4 

3 

2 

0 

0 

0 

0 

0 

0 

0 

6 

6 

2 

3 

0 

2 

0 

0 

I 

0 

0 

7 

6 

3 

2 

0 

0 

0 

0 

0 

0 

0 

8 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

9 

5 

2 

1 

0 

2 

0 

0 

0 

0 

0 

10 

8 

4 

4 

I 

2 

I 

0 

.  . 

0 

0 

II 

5 

5 

3 

3 

2 

0 

2 

0 

0 

0 

12 

3 

2 

I 

I 

I 

0 

0 

0 

I 

0 

13 

5 

4 

3 

0 

0 

I 

0 

0 

.  . 

0 

14 

6 

3 

2 

I 

.  . 

0 

0 

0 

I 

0 

15 

2 

I 

0 

0 

0 

0 

0 

0 

0 

0 

i6 

4 

2 

0 

0 

0 

4 

0 

I 

0 

0 

17 

8 

5 

3 

2 

0 

I 

0 

0 

0 

0 

i8 

5 

3 

I 

0 

0 

0 

0 

0 

0 

0 

19 

0 

2 

3 

0 

0 

0 

0 

0 

0 

0 

20 

3 

0 

I 

0 

0 

0 

0 

0 

0 

0 

21 

6 

3 

2 

I 

1 

0 

0 

I 

0 

0 

22 

2 

I 

0 

0 

0 

0 

0 

0 

0 

0 

23 

4 

2 

I 

0 

0 

0 

0 

0 

0 

0 

24 

8 

5 

3 

2 

I 

I 

0 

I 

I 

0 

25 

5 

3 

I 

I 

0 

0 

0 

0 

0 

0 

26 

3 

2 

0 

0 

0 

0 

0 

0 

0 

0 

27 

3 

0 

0 

0 

0 

0 

0 

0 

0 

0 

28 

5 

4 

4 

3 

2 

I 

0 

0 

0 

29 

6 

5 

4 

3 

2 

. . 

.  . 

.  . 

.  . 

.  . 

30 

10 

7 

6 

4 

2 

1 

0 

I 

0 

0 

31 

3 

4 

8 

4 

I 

2 

0 

0 

I 

0 

14 
Results  with  Seventh  Grade 


d 
Z 

Ui 

"5. 
a. 

< 

d. 
a 

s 

Sec.  Rep.  Apr.  21 

< 

d. 

& 

is 

< 

d. 

3 

u 
< 

d. 

d, 

& 

c75 

00 
« 

d. 

0 
IX. 

> 

« 

d. 

4) 

I 

7 

3 

0 

0 

0 

0 

0 

0 

2 

5 

4 

2 

0 

0 

0 

0 

0 

3 

4 

0 

0 

0 

0 

0 

0 

0 

4 

0 

0 

0 

0 

0 

0 

0 

0 

5 

5 

3 

0 

I 

0 

0 

0 

0 

6 

5 

5 

4 

2 

0 

2 

I 

I 

7 

14 

6 

5 

3 

0 

I 

0 

2 

8 

3 

0 

2 

I 

0 

0 

0 

0 

9 

5 

4 

3 

0 

0 

0 

I 

0 

lO 

3 

0 

2 

I 

0 

0 

0 

0 

II 

4 

0 

2 

0 

0 

0 

0 

0 

12 

2 

0 

0 

0 

0 

0 

0 

0 

13 

0 

0 

0 

0 

0 

0 

0 

0 

14 

7 

4 

3 

0 

0 

I 

0 

0 

15 
i6 

16 
16 

13 
0 

7 
4 

4 
2 

0 
0 

2 
2 

I 

0 

0 

17 

13 

5 

2 

0 

0 

0 

0 

18 

4 

2 

0 

0 

0 

0 

0 

0 

19 

18 

12 

5 

I 

0 

3 

2 

I 

20 

3 

0 

0 

0 

0 

0 

0 

0 

21 

5 

2 

0 

0 

0 

0 

I 

0 

22 

8 

3 

0 

I 

0 

1-3 

0 

0 

23 

5 

0 

2 

0 

0 

2 

0 

0 

24 

6 

4 

3 

0 

0 

0 

I 

0 

25 

8 

6 

4 

3 

0 

0 

0 

0 

26 

3 

I 

0 

0 

0 

0 

0 

0 

27 

I 

0 

0 

0 

0 

0 

0 

0 

28 

9 

4 

3 

2 

0 

0 

3 

0 

29 

13 

7 

4 

2 

0 

2 

3 

0 

30 

4 

0 

2 

I 

0 

0 

0 

0 

15 

Results  with  Eighth  Grade 


< 


iO 

UO 

o 

00 

C\J 

>» 

u 

ul 

(J 

ea 

Q. 

Q. 

o. 

^ 

< 

< 

< 

d. 

ci. 

Q. 

Q. 

4) 

0^ 

(S 

Qi 

JC 

^ 

, 

^ 

<£X 

>< 

> 

euo 

a 

uu 

c^ 

(/) 

tu 

^  ^  ^  ^  Di 

J^      ^      ^      ^       s 

a.    u.    c/)    H     u- 

I  2  I  O  O  O  O  O  O 
22      lOOOOOO 

3  4    I    2    I    o    o    o    o 

4  looooooo 
5532  10..  00 
620000000 
7  3  I  2  I  o  o  o  o 
8I2IOOOOO 
9    I    o    o    o    o    00    o 

10  20000000 

11  32000000 

12      I      0000000 

13  64300000 

14  10000000 

15  4     2..     o     O     O     O     0 

16  21000000 

17  1    0000000 

18  32200000 


16 

THE  SECOND  EXPERIMENT. 

The  facts  which  are  asked  for  in  the  following  questions 

are  the  ones  that  were  used  in  the  experiment  to  determine 

the  number  of  repetitions  that  would  be  necessary  to  fix  them 

with  maximum  certainty: 

1.  What  is  the  area  of  your  county?     About  400  square 

miles. 

2.  Where  was  it  first  settled?    At  Lehighton. 

3.  What  five  persons  are  conspicuously  connected  with  its 

settlement?  White,  Hazard,  Hauto,  Hillegas  and 
Cist. 

4.  What  nickname  was  applied  to  Robert  E.  Lee's  father? 

Light  Horse  Harry. 

5.  How  many  feet  above  sea  level  is  the  highest  point  of 

your  county?     1735   feet. 

6.  What  is  the  meaning  of  the  Indian  name  Towamensing? 

Wilderness. 

7.  What  five  persons  are  connected  with  the  walking  pur- 

chase? Edward  Marshall,  James  Yeats,  Solomon 
Jennings,  John  Penn  and  Tom  Penn. 

8.  What  was  the  most  important  sentence  uttered  by  Pat- 

rick Henry  in  the  Congress  at  Philadelphia  which 
he  attended  ?    "I  am  not  Virginian,  but  an  American." 

9.  What  was  the  value  of  the  most  important  commercial 

product  produced  in  your  locality  in  1907?  Coal, 
$9,cxx),ooo. 

10.  VVhat  is  commercially  the  most  important  river  in  the 

world?     The   Chicago. 

11.  Name  the  five  largest  cities  of  the  United  States  with 

their  approximate  population.  New  York,  4  mil- 
lions; Chicago,  2  millions;  Philadelphia,  i  million; 
Boston,  649  thousand;  St.  Louis,  602  thousand. 

12.  What  did  Paul  Revere  say  to  the  men  who  were  guard- 

ing the  house  in  which  Hancock  and  Adams  were 
sleeping?  ''Noise!  You'll  soon  hear  noise  enough, 
the  Regulars  are  coming." 

13.  How  many  men  were  lost  by  the  British  and  the  Ameri- 

cans at  the  battle  of  Lexington?  Americans  93,  Brit- 
ish 273. 

14.  What  five  geological  strata  have  their  outcrop  in  your 

locality?  Pottsville  Conglomerate,  Pocono  Sand 
Stone,  Mauch  Chunk  Red  Shale,  Coal  Measures, 
Oriskany  Sand  Stone. 

15.  Name  one  of  the  two  important  political  institutions  be- 

gun in  Virginia  in  1619.  Slavery  or  representative 
government. 

16.  What  did  Lincoln  say  when  he  heard  of  the  capture  of 

Vicksburg?  "The  father  of  waters  now  rolls  un- 
vexed  to  the  sea." 


17 

17.  About  how  many  men  did  the  United  States  lose  by  the 

Civil  War?    About  5C)0,cxx). 

18.  What  is  the  name  that  is  applied  to  the  plant  from  which 

a  large  part  of  the  coal  was  formed?  Lepidoden- 
dron. 

19.  Name  five  men  from  Pennsylvania  who  signed  the  Decla- 

ration of  Independence.  Robert  Morris,  Benjamin 
Franklin,  Benjamin  Rush,  James  Wilson,  James 
Smith,  George  Ross,  George  Taylor  and  Morton 
Clymer. 

20.  What  were  the  last  words  of  Stonewall  Jackson?     "Let 

us  cross  over  the  river  and  lie  down  under  the  shade 
of  the  trees." 

In  the  light  of  the  results  obtained  in  the  experiment  of 
the  year  before,  it  seemed  advisable  to  continue  the  work  of 
this  year  along  the  same  general  line,  but  under  somewhat 
different  conditions.  Whereas,  in  the  previous  experiment 
all  known  available  means  were  used  to  make  the  first  pres- 
entation effective  in  a  maximum  degree,  in  this  investigation 
no  attempt  at  emphasis  or  explanation  of  any  kind  was  made. 
The  facts  to  be  learned  in  the  second  experiment  were  very 
much  more  numerous  than  in  the  first,  less  likely  to  be  easily 
associated  with  any  facts  which  the  children  already  knew, 
and  much  more  likely  to  contain  difficulties  of  comorehension 
and  understanding.  Especially  unrelated  to  anything  in  ihe 
children's  experience  were  the  facts  called  for  in  question 
number  fourteen.  Much  of  what  children  are  required  to 
learn  in  school  is  like  Greek  to  them,  and  it  was  deemed  advis- 
able by  the  members  of  the  Seminar  to  determine  how  the 
learning  of  such  facts  as  to  them  have  probablv  no  meaning 
or  but  little  meaninp-.  compared  with  the  learning  of  facts  such 
as  are  readily  associated  by  them  or  were  made  associable  by 
the  exDerimenter.  In  the  first  experiment  care  was  taken  to 
select  only  such  facts  as  seemed  essential  or  would  be  taught 
as  part  of  the  regular  content  of  the  year.  In  the  second  in- 
vestigation an  attempt  was  made  to  have  the  facts  as  hetero- 
geneous as  possible  and  as  numerous  as  could  be  repeated  dur- 
ing one  continuous  period  of  mental  effort.  In  the  first  ex- 
periment the  facts  were  relatively  few  and  presented  in  the 
most  effective  manner  known,  in  connection  wnth  the  regular 
work  of  the  class  in  the  subject  to  which  they  belonged ;  in 
the  second  they  are  quite  heterogeneous,  as  numerous  as  pos- 
sil^le,  almost  nonsense  syllables  in  many  cases,  and  presented 
without  instruction  or  explanation. 

The  questions  numbered  i.  5,  Q,  \y,  require  one  number 
for  an  answer,  while  13  requires  two.  The  questions  num- 
bered 2,  6,  10  and  18  are  answered  with  one  word  as  also  is 
number  !=;.  Numbers  .-^  and  7  require  the  nanibs  of  five  in- 
dividuals, but  number  t  i  needs  for  its  answer  /the  najHCf  of 


18 
five  cities  with  which  it  was  supposed  that  each  child  in- 
cluded in  the  test  was  fairly  familiar,  and  after  the  names  of 
these  cities  he  was  required  to  write  the  numbers  which  repre- 
sented their  approximate  population.  Three  of  these  numbers 
he  was  requested  to  write  by  prefixing  the  figures  4,  2  and  i 
before  the  word  million,  and  the  other  two  of  the  five  num- 
bers required  to  answer  question  number  11,  it  was  necessary 
for  him  to  write  649  and  602  before  the  word  thousands.  Ques- 
tion number  14  is  answered  by  five  terms  all  of  which  were 
new  to  the  children,  rather  difficult  to  spell,  and  about  as  diffi- 
cult to  remember  for  most  of  the  children  as  nonsense  sylla- 
bles usually  are.  As  an  answer  for  question  number  19,  the 
five  names  of  five  signers  of  the  Declaration  of  Independence 
which  were  placed  first  in  the  list  were  most  frequently  writ- 
ten. With  at  least  three  of  these  all  of  the  children  in  the  test 
were  familiar,  and  it  is  quite  probable  that  the  children  had 
met  all  of  the  names  at  some  time  during  their  school  careers. 
Every  time  that  the  answer  for  number  19  was  repeated  the 
names  of  the  eight  men  were  repeated,  but  the  children  were 
never  required  to  write  more  than  five. 

Question  number  4,  though  grouped  with  the  quotations, 
is  in  fact  only  a  nick  name  of  three  words  and  each  of  these 
is  easily  remembered.  The  answer  to  questions  number  8, 
12,  16  and  20,  is  a  short  quotation  associable  with  facts 
with  which  the  children  are  already  fairly  familiar,  but  is  the 
expression  of  an  idea  in  a  form  that  was  entirely  new.  The 
general  nature  of  the  questions  may  be  readily  seen  from  the 
following  summary : 

Numbers  i,  5,  9,  13,  17  are  answered  by  a  figure. 

Numbers  2,  6,  10,  15,  18  are  answered  by  one  word. 

Numbers  3,  7,  11,  14,  19  are  answered  by  five  words. 

Numbers  4,  8,  12,  16,  20  are  answered  by  a  quotation. 

The  directions  which  were  given  to  the  various  teachers 
for  conducting  the  experiment  were  as  follows: 

1.  The  teacher  will  read  the  first  question. 

2.  The  teacher  will  read  the  answer  to  the  first  question. 

3.  The  pupils  will  write  the  answer  to  the  first  question 
on  slips  of  paper  prepared  for  the  purpose. 

4.  The  teacher  will  read  the  second  question. 

5.  The  teacher  will  read  the  answer  to  the  second  ques- 
tion. 

6.  The  pupils  will  write  the  answer  to  the  second  ques- 
tion. 

7.  The  teacher  will  read  the  third  question. 

8.  The  teacher  will  read  the  answer  to  the  third  question. 

9.  The  pupil  will  write  the  answer  to  the  third  question. 

10.  Thus  the  teacher  will  continue  to  read  the  questions 
and  then  the  answers,  and  the  pupils  will  thus  continue  to  write 
the   answers  until   all  the   questions   and   answers  have   been 


19 
read  and  all  the  answers  have  been  written.     The  papers  will 
then  always  be  sent  to  the  principal. 

11.  The  teacher  will  then  collect  the  papers  on  which 
the  answers  were  written  and    send  them  to  the  principal. 

12.  At  all  later  repetitions  the  teacher  will  read  the  ques- 
tions only,  but  always  in  the  order  in  which  they  are  number- 
ed. The  pupils  will  write  the  answer  to  each  question  imme- 
diately after  it  has  been  read. 

13.  Thus  they  will  continue  until  the  facts  are  learned; 
the  principal  will  always  fix  the  date  at  which  a  repetition  of 
tlie  facts  is  to  be  made. 

14.  At  the  close  of  each  repetition,  after  the  papers  have 
been  collected  the  teachers  will  again  read  the  question  and 
answers  in  such  a  way  that  the  reading  of  each  question  will 
be  followed  by  the  reading  of  the  answer  in  regular  succession. 

The  directions  were  given  in  this  form  in  the  hope  of 
securing  uniformity.  To  have  each  child  write  the  answer  as 
it  was  presented  to  him  immediately  after  the  first  question 
was  read  at  the  first  presentation  gave  all  an  equal  opportunity 
to  get  the  impression  clearly,  and  by  writing  it  there  was 
maximum  certainty  that  the  impression  was  received  correct- 
ly. When  the  answer  that  was  required  had  once  been  defi- 
nitely fixed,  the  likelihood  was  that  each  following  repetition 
would  bring  the  response  required.  Oral  repetition  was  prac- 
tically impossible  because  of  the  time  it  would  have  required. 
It  was  deemed  wise  to  repeat  the  correct  answer  to  each  of 
the  cpiestions  immediately  after  the  children  had  maae  an 
attempt  to  answer  them,  since  it  was  supposed  that  each  child 
would  listen  with  close  attentioa  for  the  answers  which  he 
was  conscious  of  having  missed.  Repeating  the  questions  and 
answers  after  each  repetition  had  the  advantage  of  making 
the  repetition  uniform  for  each  individual  of  the  group,  absent 
(»ncs,  however  excepted.  On  the  sheets  .containing  the  results 
absentees  are  indicated  by  an  addition  sign. 

It  is  impossible  to  determine  just  how  faithfully  the  direc- 
tions were  followed.  In  the  high  school  the  experimenter  him- 
self was  present  at  each  repetition,  and  the  probability  is  that 
the  results  on  the  high  school  sheet  represent  the  honest  effort 
of  the  group  during  the  time  the  experiment  was  in  progress 
according  to  the  directions  as  given.  Just  how  to  account  for 
such  phenomenal  improvements  as  a  drop  from  twenty-eight 
errors  to  five,  or  from  thirty  to  one  as  is  indicated  in  numbers 
18  ^nd  19,  is  rather  perplexing.  That  it  may  have  been  possible 
for  these  individuals  to  have  made  a  copy  of  the  answers  as 
they  were  being  repeated  by  the  experimenter,  is  true,  but  not 
likely.  Especial  vigilance  on  the  part  of  the  three  teachers  in 
the  room  at  the  time  would  probably  have  detected  the  indi- 
viduals writing  had  any  of  them  attempted  it.  The  individuals 
arc  apt  learners  and  it  is  my  belief  that  they  simply  remem- 


20 
bered  the  facts. 

The  intervals  between  the  repetitions  were  by  no  means 
uniform.  As  stated  before,  the  first  experiment  conducted 
in  connection  with  work  the  Pedagogical  Seminar  had  to  do 
with  the  learning  of  facts  that  would  ordinarily  occur  in  con- 
nection with  the  regular  school  work  under  ordinary  normal 
school  conditions  as  nearly  as  possible.  The  second  differed 
from  the  first  in  that  the  facts  to  be  learned  were  much  more 
numerous  and  had  but  little  connection  with  the  regular  school 
work,  and  were  presented  without  any  attempt  to  make  the 
presentation  as  effective  as  possible. 

In  the  results  that  follow,  the  number  of  pupils,  the  num- 
ber of  errors  and  the  date  of  the  repetition  is  indicated  as  in 
the  first  experiment.  The  record  marked  Sixth  and  Seventh 
grade  was  made  by  a  group  of  chidren  in  these  grades  ihat 
were  taught  in  the  same  room  by  the  same  teacher.  Those 
marked  A  Grammar  represent  the  results  of  the  efforts  of  the 
eighth  grade  pupils,  while  those  marked  Hauto  were  made  by 
the  grades  indicated,  all  being  taught  in  the  same  room  by  one 
teacher. 

The  result  sheets  for  the  high  school  and  the  seventh 
grade  explain  themselves,  since  all  the  factors  recorded  are 
indicated  just  as  on  the  previous  result  sheets.  The  sheet 
marked  Suminary  of  Errors  is  a  tabulation  of  the  errors  that 
were  made  by  the  various  groups  whose  record  in  the  second 
experiment  have  preceded.  The  numbers  and  letters  in  the 
left  hand  column  indicate  the  number  and  part  of  the  various 
(juestions.  The  numbers  in  the  succeeding  columns  tell  how 
many  errors  were  made  by  the  groups  in  answering  that  par- 
ticular qrestion  whose  number  is  indicated  by  the  figures  in 
the  left  hand  column.  The  respective  groups  and  the  number 
of  pupils  that  were  in  each  is  indicated  at  the  top  of  each 
column.  The  number  in  the  right  hand  column  indicates  the 
number  of  errors  that  were  made  in  answering  the  questions 
indicated  by  the  entire  group.  On  the  sheet  marked  "Facts 
Arranged  according  to  Number  of  Errors"  the  figure  in  the 
first  column  indicates  the  number  of  the  question,  the  number 
in  the  second  column  the  entire  number  of  errors  that  were 
made  with  the  particular  question,  and  in  the  third  column 
are  the  answers  desired,  or  a  word  describing  the  answer  that 
was  exepected  to  be  given. 

On   averaging  the  number   of   repetitions   that   were  re 
quired  to  learn  the  facts  by  the  various  individuals  the  follow- 
ing facts  appeared : 

Average  number  of  repetitions  required  by  high  school 
pupils  6. 

Average  number  of  repetitions  required  by  sixth  and 
seventh  grade  7.5. 

Average  number  of  repetitions  required  by  seventh  grade 


21 

7-5. 

Average  number  of  repetitions  required  by  A  Grammar 
grade  6. 

Average  number  of  repetitions  required  by  Hauto  Pupils 
6. 

The  conclusion  would,  from  this,  be  justifiable  that  the 
facts  were  learned  in  about  seven  repetitions. 


22 
HIGH   SCHOOL 


O) 

0 

^ 

CM 

00 

^ 

00 

lO 

00 

^      J^ 

,,^ 

1—' 

»-^ 

'-^ 

■•—' 

CNl 

— ' 

»— • 

—    CQ 

•a 

3 

c2i 

-• 

'Z 

^ 

"z 

" 

(A 

' 

' 

-     - 

'  I 

32 

15 

5 

0 

2 

4 

3 

3 

0 

2 

32 

17 

13 

II 

4 

6   9 

3 

32 

22 

23 

15 

19 

18 

17 

13 

3   5 

4 

5 

29 
15 

17 
8 

18 

23 

3 

4 

6 

5 

4 

4 

4  .. 

6 

. . 

14 

8 

7 

II 

. . 

14 

II 

I 

7 

31 

13 

6 

3 

8 

13 

7 

7 

5 

11 

9 

3 

4 

0 

9 

17 

I 

I 

0 

0 

0 

lO 

16 

I 

0 

0 

0 

0 

II 

18 

2 

2 

. . 

4 

0 

12 

18 

II 

2 

0 

. . 

I 

13 

3. 

0 

0 

I 

0 

1 

. 

14 

24 

0 

0 

0 

0 

0 

15 

19 

7 

I 

0 

0 

0 

16 

16 

7 

4 

0 

17 

20 

15 

9 

II 

16 

9 

8 

3 

0 

18 

28 

5 

0 

0 

0 

0 

0 

19 

30 

I 

0 

0 

0 

0 

0 

20 

23 

0 

0 

0 

. . 

0 

0 

21 

18 

. . 

. . 

2 

8 

4 

2 

22 

5 

I 

0 

0 

I 

I 

I 

^Z 

13 

8 

2 

0 

0 

0 

0 

24 

27 

6 

0 

I 

I 

0 

25 

31 

13 

5 

2 

2 

26 

13 

. . 

. . 

0 

0 

0 

27 

31 

17 

6 

I 

I 

I 

0 

» 

28 

12 

0 

0 

0 

0 

0 

0 

29 

15 

19 

I 

3 

I 

2 

30 

31 

19 

4 

I 

0 

0 

31 

17 

0 

0 

4 

I 

32 

31 

3 

0 

33 

29 

22 

9 

0 

8 

5 

4 

2 

34 

37 

28 

15 

9 

4 

4 

2 

1 

35 

. . 

II 

12 

. . 

5 

6 

6 

2 

36 

29 

16 

10 

6 

4 

3 

4 

I 

37 

10 

3 

0 

4 

2 

38 

22 

I 

I 

0 

0 

0 

2 

39 

24 

2 

5 

I 

40 

34 

15 

9 

2 

6 

7 

5 

I 

41 

29 

16 

14 

9 

9 

II 

4 

5 

I 

42 

23 

7 

10 

13 

3 

2 

^ 

u^. 


23 

V 

("■  n 

A  GRAMMAR 

X 

v.C4i_^ 

1  r  c  f . 

O) 

0 

OJ 

fC 

CO 

to 

x 

05 

,^ 

'— 

eg 

'— ' 

'5. 

c2i 

:; 

;; 

- 

- 

^ 

- 

- 

I 

15 

15 

10 

I 

14 

7 

I 

2 

13 

6 

2 

8 

II 

8 

6 

I 

3 

7 

2 

9 

15 

I 

4 

2 

I 

0 

0 

3 

3 

0 

5 

15 

2 

0 

0 

5 

0 

6 

34 

18 

13 

14 

I 

7 

22 

3 

2 

3 

0 

8 

4 

5 

0 

0 

0 

0 

0 

9 

20 

7 

0 

0 

2 

I 

TO 

15 

5 

I 

0 

0 

I 

II 

17 

8 

2 

3 

2 

0 

12 

7 

I 

6 

3 

2 

13 

II 

3 

0 

0 

0 

0 

14 

3 

0 

0 

0 

2 

15 

4 

I 

0 

0 

0 

0 

i6 

14 

2 

I 

0 

I 

17 

19 

's 

.. 

2 

i8 

II 

9 

2 

I 

3 

2 

19 

20 

19 

7 

II 

'6 

I 

20 

26 

14 

5 

3 

II 

5 

2 

21 

13 

I 

0 

0 

0 

4 

2 

22 

9 

2 

2 

0 

I 

3 

0 

HAUTO.    5th        6th 


7th 


05 

0 

^ 

m 

05 

^ 

CO 

05 

"a 

JD 

- 

- 

- 

- 

- 

- 

3 

t2i 

% 

I 

6 

19 

15 

15 

8 

10 

8 

2 

2 

16 

9 

0 

2 

0 

3 

8 

10 

I 

I 

2 

0 

4 

8 

0 

0 

I 

0 

0 

0 

0 

5 

22 

21 

5 

9 

I 

0 

14 

6 

21 

6 

14 

8 

8 

0 

0 

0 

7 

9 

14 

5 

0 

0 

0 

I 

0 

8 

7 

2 

I 

2 

0 

0 

0 

0 

9 

4 

0 

0 

0 

0 

0 

I 

4 

10 

7 

0 

0 

I 

0 

I 

0 

0 

II 

15 

0 

0 

I 

I 

0 

0 

12 

5 

2 

0 

0 

0 

0 

0 

I 

13 

15 

0 

0 

0 

0 

I 

14 

12 

8 

I 

0 

2 

0 

0 

15 

18 

17 

II 

II 

5 

6 

10 

5 

16 

19 

9 

0 

.2 

0 

0 

0 

I 

17 

14 

10 

0 

0 

2 

0 

18 

31 

29 

29 

9 

5 

5 

19 

18 

3 

8 

I 

0 

2 

0 

0 

20 

24 

22 

19 

16 

6 

5 

7 

21 

8 

I 

0 

0 

0 

22 

19 

10 

6 

5 

8 

6 

5 

7 

23 

6 

3 

0 

0 

0 

0 

0 

24 

14 

16 

II 

15 

12 

10 

8 

12 

25 

5 

I 

0 

0 

I 

0 

0 

0 

26 

9 

17 

I 

10 

4 

I 

0 

I 

27 

14 

2 

3 

7 

I 

0 

2 

0 

28 

14 

17 

0 

2 

5 

3 

2 

29 

8 

0 

0 

0 

0 

0 

0 

0 

30 

12 

6 

2 

0 

I 

0 

0 

0 

24: 

Sixth  and  Seventh  Grade 
»-  CNJ         lO         r^  00 


a. 

3 

0) 

: 

:: 

>* 

- 

c3 

- 

:: 

J 

Ou 

u: 

^ 

I 

24 

15 

7 

2 

8 

7 

8 

,  , 

0 

2 

36 

15 

14 

14 

7 

15 

8 

II 

I 

3 

18 

6 

5 

3 

5 

9 

3 

2 

4 

27 

II 

7 

5 

5 

18 

9 

0 

5 

12 

6 

8 

6 

9 

. . 

5 

0 

6 

38 

27 

29 

24 

29 

36 

32 

33 

33 

7 

32 

15 

12 

10 

8 

15 

12 

7 

4 

8 

35 

20 

9 

15 

12 

9 

9 

31 

II 

9 

6 

19 

. . 

10 

5 

9 

10 

27 

10 

7 

5 

8 

13 

10 

5 

II 

26 

II 

5 

7 

. . 

. , 

, , 

12 

24 

6 

0 

0 

0 

3 

0 

13 

28 

4 

6 

5 

2 

3 

0 

14 

27 

3 

8 

7 

5 

2 

15 

26 

5 

5 

3 

4 

3 

2 

i6 

15 

3 

2 

0 

0 

. . 

0 

i; 

18 

I 

0 

0 

0 

0 

0 

i8 

14 

0 

0 

0 

0 

2 

19 

14 

3 

2 

0 

0 

5 

I 

20 

21 

3 

5 

3 

3 

2 

21 

24 

3 

3 

2 

3 

2 

22 

14 

0 

0 

0 

0 

2 

23 

14 

5 

I 

0 

0 

I 

24 

12 

7 

4 

. , 

. . 

18 

12 

0 

25 

36 

26 

29 

16 

20 

25 

7 

, , 

I 

26 

22 

13 

5 

5 

10 

4 

0 

27 

3 

0 

I 

0 

4 

0 

0 

2 

28 

25 

8 

0 

2 

0 

7 

3 

I 

29 

23 

7 

4 

2 

2 

4 

7 

2 

25 
Seventh  Grade 


a. 

- 

- 

- 

- 

OS 

' 

' 

^   ^ 

I 

27 

19 

15 

. . 

8 

13 

13 

. . 

10   5 

2 

27 

20 

19 

20 

10 

15 

18 

6 

9   4 

3 

24 

26 

2 

4 

27 

17 

12 

12 

15 

4 

9 

3   0 

5 

27 

25 

16 

21 

3 

4 

10 

5 

I 

6 

28 

23 

17 

20 

5 

10 

9 

7 

6   I 

7 

29 

20 

15 

17 

9 

10 

. . 

. . 

4   I 

8 

29 

26 

22 

24 

I 

.  . 

12 

3 

I 

9 

34 

28 

14 

17 

8 

3 

I 

lO 

28 

19 

5 

12 

2 

II 

. . 

. . 

. . 

. , 

. , 

I 

0 

12 

26 

18 

8 

9 

0 

10 

I 

13 

37 

30 

19 

23 

7 

8 

2 

14 

5 

2 

I 

. . 

. . 

I 

15 

20 

9 

7 

. . 

0 

0 

16 

28 

16 

18 

25 

I 

0 

17 

6 

7 

5 

0 

I 

18 

18 

14 

I 

7 

0 

19 

24 

14 

6 

10 

9 

8 

I 

20 

27 

24 

8 

19 

15 

0 

21 

27 

22 

21 

20 

8 

12 

4 

2 

22 

27 

18 

19 

. . 

4 

9 

6 

0 

23 

34 

24 

21 

6 

.8 

8 

0 

24 

25 

17 

10 

II 

2 

12 

7 

0 

25 

22 

II 

7 

9 

0 

8 

5 

0 

26 

30 

19 

15 

II 

II 

I 

27 

28 

20 

12 

13 

2 

. . 

12 

. . 

6   2 

28 

32 

20 

25 

20 

6 

15 

8 

I 

29 

28 

22 

15 

. . 

6 

. . 

13 

0 

30 

28 

25 

14 

19 

2 

9 

7 

0 

31 

21 

II 

17 

4 

6 

5 

4 

I 

32 

27 

21 

14 

13 

5 

15 

6 

6 

2 

33 

29 

15 

9 

. . 

44 

6 

8 

6 

0 

34 

25 

20 

18 

16 

9 

16 

7 

r- 

2 

35 

29 

16 

15 

12 

4 

II 

11 

5 

0 

36 

26 

14 

13 

13 

26 

12 

8 

3 

0 

37 

38 

27 

26 

25 

7 

20 

12 

7 

I 

38 

33 

28 

19 

16 

12 

18 

2 

39 

30 

27 

18 

20 

7 

13 

8 

7 

2 

26 

Summary  of  Errors 


u 

0 

uT 

0 

t^ 

3 

.  •  3 

0  3 

t^  3 

tj  3 

djj  3 

C3X) 

cS"^ 

.  a- 

^'^ 

o"^ 

cd"^ 

;;:  og 

^  05 

-£  C2 

O) 

^  <M 

-  0 

X    rt 

DQ  ro 

CO  fO 

CO  eg 

<  CNJ 

10  CO 

I 

8 

12 

8 

5 

4 

I 

38 

2 

14 

39 

15 

4 

5 

I 

78 

3a 

20 

51 

6 

24 

10 

4 

115 

b 

38 

83 

21 

29 

17 

2 

190 

c 

44 

108 

27 

34 

II 

4 

227 

d 

56 

III 

40 

64 

21 

6 

288 

e 

59 

80 

41 

66 

17 

9 

272 

4 

7 

II 

4 

0 

0 

I 

23 

5 

46 

75 

13 

46 

7 

6 

193 

6 

14 

17 

3 

II 

2 

2 

49 

7a 

47 

96 

55 

43 

17 

13 

271 

b 

57 

no 

81 

51 

18 

17 

334 

c 

.  55 

128 

100 

64 

32 

18 

377 

d 

59 

146 

82 

59 

31 

20 

317 

e 

60 

107 

58 

57 

32 

27 

341 

8 

8 

21 

14 

10 

16 

8 

76 

9 

22 

50 

42 

30 

6 

44 

194 

10 

5 

4 

7 

12 

3 

5 

36 

iia 

35 

79 

52 

30 

9 

13 

218 

b 

63 

123 

87 

42 

19 

26 

360 

c 

68 

133 

73 

44 

23 

34 

375 

d 

77 

190 

136 

72 

28 

43 

546 

e 

98 

166 

125 

72 

39 

45 

545 

12 

13 

II 

•  5 

4 

5 

10 

48 

13a 

33 

26 

5 

13 

7 

12 

96 

b 

51 

47 

32 

21 

33 

26 

210 

14a 

'43 

49 

46 

16 

6 

41 

201 

b 

66 

91 

68 

19 

16 

52 

312 

c 

72 

115 

65 

34 

II 

62 

359 

d 

85 

127 

76 

52 

14 

74 

428 

e 

84 

108 

64 

58 

22 

77 

413 

15 

56 

14 

42 

28 

-  5 

\2 

157 

16 

32 

52 

56 

30 

25 

35 

230 

17 

67 

122 

93 

34 

26 

34 

384 

18 

40 

72 

63 

34 

5 

10 

224 

19a 

35 

90 

62 

33 

21 

35 

276 

b 

47 

136 

87 

43 

23 

40 

376 

c 

60 

136 

98 

68 

29 

37 

398 

d 

77 

157 

109 

74 

40 

56 

513 

e 

74 

125 

82 

75 

41 

59 

456 

20 

15 

23 

16 

12 

4 

15 

95 

27 

Facts  arranged  according  to  number  of  errors 

Nickname. 

Chicago. 

One  Number. 

One  Number. 

Wilderness. 

Quotation. 

Familiar  Narfie. 

Quotation. 

Number. 

Packer  (town). 

Slavery  or  Rep.   Gov. 

Hauto(town). 

Number. 

Number. 

Potts.  Cong.  (town). 

Number. 

City  &  Number. 

Term  (Rhododendron). 

Hazard   (Town). 

Quotation. 

Marshall   (unfamiliar  name). 

Cist   (unfamiliar  name). 

Robert  Morris. 

Hillegas  (unfamiliar  name), 

Pocono  Sandstone. 

James  Yeats  (unfamiliar  name). 

Solomon  Jennings  (unfamiliar  name) 

Mauch  Chunk  Red  Shale. 

Chicago,  2  mill. 

Benjamin  Rush. 

Phila.,   I  mill. 

500,000. 

John  Penn. 

Franklin. 

Solomon  Jennings. 

Oriskany  Sandstone. 

Coal   Measurer   (familiar). 

James  Smith. 

Morton  Clymer. 

St.  Louis,  649  thous. 

Boston,  602  thous. 


4 

23 

10 

36 

I 

38 

12 

48 

6 

49 

8 

76 

2 

78 

20 

95 

13a 

96 

3a 

115 

15 

157 

3b 

190 

5 

193 

9 

194 

14a 

201 

13b 

210 

iia 

218 

18 

224 

13c 

227 

16 

230 

7a 

271 

3e 

2^2 

19a 

276 

3d 

288 

14b 

312 

7b 

334 

7e 

341 

14c 

359 

lib 

360 

19b 

376 

lie 

375 

17 

384 

7d 

397 

19c 

398 

7c 

399 

14c 

413 

I4d 

428 

I9e 

456 

i9d 

513 

lie 

545 

iid 

546 

28 
THE  THIRD  EXPERIMENT. 

In  the  light  of  the  results  obtained  in  the  previous  exper- 
iments, it  seemed  advisable  to  try  to  determine  how  the  learn- 
ing of  forgotten  facts  compared  with  the  results  in  former 
experiments.  In  order  to  make  this  comparison,  the  following 
list  of  questions  was  selected  to  be  used  with  the  pupils  in  the 
high  school.  All  the  children  now  in  this  school  were  taught 
in  the  A  Grammar  room  by  the  same  teacher.  He  declares 
that  every  pupil  who  passed  through  his  room  at  one  time 
knew  the  facts  called  for  in  the  questions. 

The  experiment  was  conducted  by  the  experimenter  in 
accordance  with  the  directions  given  for  the  second  experiment, 
except  that  there  was  no  first  presentation  of  the  facts.  It 
was  assumed  that  each  pupil  was  familiar  with  the  facts  and 
the  first  exercise  of  this  experiment  was  conducted  just  as 
was  the  first  repetition  in  the  first  and  second  experiment.  The 
interval  was  arbitrarily  fixed  at  a  week,  though  the  results 
would  no  doubt  have  been  somewhat  better  had  the  interval 
been  shorter.  The  number  of  questions  was  so  arranged  as 
to  require  the  writing  of  about  as  many  facts  as  were  required 
in  the  second  experiment.  This,  it  was  thought  would  make 
the  matter  of  comparison  somewhat  simpler.  The  questions 
used  follow : 

I.     I.  How    many    degrees    from   the   north   pole   to   the 
equator  ?    90. 

2.  In  what  year  was  the  ordinance  passed  which  re- 
lated to  the  government  of  the  Northwest  Territory? 

1787. 

3.  In  what  year  was  Jamestown  settled?      1G09 

4.  When  was  the  Pacific  Ocean  discovered?     15 13. 

5.  In  what  year  was  the  Mexican  War  begun?  1848. 
II.     I.  In   whose   administration   did  the   President   refuse 

to  sign  the  Bank  Charter?    Jackson's. 

2.  In  whose  administration  was  Louisiana  purchased? 
Jefiferson's. 

3.  In    whose    administration    was    the    Second    War 
with  England?    Madison's. 

4.  In  what  war  was  the  Battle  of  Long  Island  fought  ? 
Revolutionary. 

5.  To    what    party    did    Thomas    Jefferson    belong? 
Anti  Federalists. 

III.     I.  What  large  island  south  east  of  Africa?    Madagas- 
car. 

2.  What  ocean  south  of  Hindoostan?     Indian. 

3.  What  mountain  range  between  Europe  and  Asia? 
Ural. 

4.  What  river  between  the  United  States  and  Canada? 
St.  Lawrence. 

5.  What   cape   at  the   southern   extermity  of    South 
America?     Cape  Horn. 


29 

IV.  I.  By  whom  was  South  America  discovered?    Colum- 

bus. 

2.  Who  probably  was  the  originator  of  the  Monroe 
Doctrine?    J.  Q.  Adams. 

3.  By   what   title   is   the   ruler   of   Turkey   known? 
Sultan. 

4.  How  many  years  did  Washington  serve  as  Pres- 
ident?   Eight. 

5.  What  leader  crushed  the  Creeks  and  Seminoles 
in  Florida?    Jackson. 

V.  I.  Name  in  their  order  five  rebellions  that  have  occur- 

red in  our  history,     (a)   Claybourne's,   (b)   Bacon's, 
(c)  Whiskey,  (d)   Dorr,  (e)  Great  Rebellion. 
VI.     For  what  achievement  are  the  following  men  noted? 

1.  Thomas  A.  Edison. 

2.  S.  F.  B.  Morse. 

3.  Geo.  B.  Meade. 

4.  Eli  Whitney. 

5.  Elias  Howe. 

VII.  Beginning  with  Florida  name  five  States  in  succession 
that  border  on  the  Atlantic  Ocean,  Florida,  Georgia, 
South  Carolina,  North  Carolina  and  Virginia. 

VHI.     I.  What  is  the  capital  of  Germany?     BerHn. 

2.  What  is  the  capital  of  Cuba?     Havana. 

3.  In  what  country  is  Sydney  located?  New  South 
Wales. 

4.  In  what  country  is  Buenos  Ayres  located  ?  Argen- 
tine RepubHc. 

5.  In  what  country  is  Venice  located?    Italy. 

IX.     State  briefly  the  substance  of  the  Monroe  Doctrine. 

For  any  Euronean  country  to  try  to  gain  dominion 
in  America  will  be  considered  an  unfriendly  act  by 
the  United   States. 

Of  the  forty-one  possible  errors  the  best  record  was  made 
by  a  boy  who  wrote  all  of  the  answers  correctly  except  seven, 
and  the  poorest  record  was  made  by  a  girl  who  missed  thirty- 
pix.  No  one  was  more  surprised  than  the  experimenter  to 
learn  that  so  many  of  the  facts  once  well  known  and  quite 
familiar  should  so  soon  be  forgotten.  The  teacher  who  taught 
the  pupils  while  they  were  in  the  Grammar  School  was  equally 
surprised. 

Thirty  of  the  individuals  in  the  test  learned  to  write  the 
forty-one  facts  by  having  two  repetitions ;  the  remaining  thir- 
teen required  three.  The  ease  and  readiness  with  which  they 
were  recalled  is  perhaps  as  surprising  as  the  fact  that  so  large 
a  part  of  the  educational  content,  which  was  considered  well 
taught  and  well  known,  should  have  been  so  easily  forgotten. 

In  the  results  which  follow,  the  numbers  in  the  first  col- 
umn denote  the  number  of  pupils  and  the  other  numbers  indi- 
cate the  errors  made  in  the  various  repetitions.  With  the  pu- 
pils after  whose  number  there  is  nothing  in  the  third  column 
the  facts  were  learned  in  two  repetitions. 


30 
Fifth  Grade         Facts  of  Experiment 


n        ^  -  ^ 


§•        c: 

c 

C3 

C3 

£        ^ 

•—5 

^ 

^ 

I     8 

41-3 

0 

0 

2     7  1-3 

II 

61 

-3     0 

3  12  1-3 

32-3 

4 

I 

4  17 

7 

5 

32-3 

5     8  2-3 

51-2 

0 

I 

6    62-3 

I 

I 

2 

7    9  1-3 

4 

I 

2 

8     8  2-3 

I 

0 

0 

9     8  1-3 

0 

0 

0 

lo  10  1-3 

2 

0 

0 

n     82-3 

0 

0 

0 

12     62-3 

0 

1-2 

0 

13  13  1-2 

2  2-3 

4 

5 

14  12  1-2 

2 

I 

0 

15     65-6 

I 

0 

0 

16  12  1-3 

0 

I 

I 

17  14  1-2 

0 

41 

-3     3 

18  13  1-3 

0 

I 

I 

19  12 

5 

2-3 

2 

20  12  1-3 

6 

7 

6 

21     61-3 

0 

2 

0 

22  142-3 

I 

2  I 

-3     0 

23     9  1-2 

0 

3 

0 

24  20 

7 

7 

41-3 

25   13  1-3 

0 

I 

, . 

26     8 

0 

0 

1-3 

27  19 

91-3 

II 

102-3 

28  142-3 

0 

8i- 

-3     3 

29   16 

I 

3 

I 

30  13  1-3 

6 

5 

I 

31   172-3 

8 

12 

61-3 

32     6  2-3 

0 

I 

2 

33   15 

0 

I 

0 

34  16 

21-3 

4 

3 

35   17 

0 

[-2 

4 

416  1-2  905-6 

98 

631-3 

31 

Results  of  Repetition  of  Facts  Used  in 
Third  Experiment 


^ 

^ 

^ 

d 
2 

z 

I 

12 

10 

4 

2 

II 

10 

13 

3 

4 

9 

4 

13 

6 

1 

5 

9 

7 

0 

6 

5 

5 

I 

7 

15 

8 

13 

I 

0 

9 

20 

13 

lO 

10 

4 

I 

II 

11 

5 

2 

12 

5 

7 

I 

13 

13 

6 

18 

14 

7 

6 

2 

15 

4 

2 

I 

i6 

8 

10 

9 

17 

4 

2 

0 

i8 

15 

7 

2 

19 

14 

14 

17 

20 

16 

II 

12 

21 

5 

4 

0 

22 

9 

4 

5 

23 

10 

13 

12 

24 

10 

I 

2 

25 

7 

I 

0 

26 

10 

12 

4 

27 

10 

II 

13 

28 

9 

4 

29 

13 

I 

6 

30 

9 

7 

31 

5 

7 

5 

32 

8 

I 

I 

33 

5 

4 

0 

34 

9 

3 

5 

35 

9 

8 

II 

36 

15 

15 

. . 

37 

8 

14 

8 

38 

3 

0 

0 

39 

8 

7 

40 

20 

12 

41 

14 

12 

11 

42 

12 

. . 

18 

397 

284 

197 

S2 

THE  FOURTH  EXPERIMENT. 
In  order  to  determine  the  interval  at  which  facts  once 
well  known  should  be  repeated  in  order  that  they  may  not  be 
forgotten,  it  seemed  expedient  to  use  the  facts  that  had  been 
learned  in  the  previous  experiments.  The  facts  used  in  the 
second  were  at  one  time  known  to  the  children,  and  the  ex- 
perimenter had  positive  knowledge  of  the  conditions  under 
which  they  were  learned.  It  was  therefore  arranged  to  call 
for  a  repetition  of  these  facts  at  varying  intervals. 

Ihe  results  of  these  repetitions  follow.  They  are  headed 
respectively:  Results  with  H:gh  School,  Results  with  A 
Grammar  School,  and  Results  with  Seventh  Grade,  A  and  B 
Divisions. 

Since  the  facts  of  the  second  experiment  were  rather 
difficult  to  learn,  and  since  the  conditions  under  which  they 
would  be  forgotten  would  probably  differ  somewhat  from  the 
manner  of  forgetting  things  learned  under  ordinary  school 
conditions,  it  was  decided  that  in  this  attempt  at  determining 
the  length  of  the  interval,  it  would  be  well  to  use  also  the  facts 
of  the  third  experiment  which  were  regularly  learned  as  school 
lessons  as  well  as  the  facts  used  with  the  fifth  grade  in  ihe 
first  experiment.  The  fifth  grade  had,  with  seeming  ease, 
learned  the  facts  presented  to  them  in  what  seemed  to  be  a 
remarkably  short  time  and  there  existed  an  interval  of  twenty 
months  since  the  last  repetition. 

The  results  of  the  last  mentioned  repetitions  will  also  be 
found  on  the  following  sheets:  The  sheet  containing  the  re- 
sults obtained  with  facts  of  experiment  three  are  so  designated, 
and  the  results  obtained  with  what  were  fifth  grade  pupils 
when  the  facts  were  given  in  the  first  experiment,  are  headed 
Fifth  Grade  of  1907,  Experiment  i  ;  though  it  must  not  be  for- 
gotten that  these  pupils  are  now  seventh  grade  children,  and 
that  in  the  meanwhile  they  have  not  studied  the  Geography  of 
South  America  as  a  regular  school  lesson. 

The  sheet  containing  a  summarization  of  the  results  has 
the  summary  of  the  results  obtained  with  each  group,  sim- 
ilarly designated. 

A  glance  at  the  Summary  of  Results  will  show  the  fact 
that  the  accuracy  of  the  average  of  errors  is  dependent  upon 
the  children  who  were  absent.  If  the  absentees  were  indi- 
viduals who  usually  had  more  than  the  average  number  of 
errors,  the  general  average  was  proportionately  lowered,  and 
if  the  absentees  were  those  who  usually  made  less  than  the 
average  number  of  errors,  this  general  average  was  increased, 
since  their  absence  would  diminish  the  divisor  by  one  and  have 
but  little  effect  upon  the  dividend.  Since,  however,  in  no  case 
the  absence  of  any  child  affected  the  general  average  more  than 
I,  it  was  considered  by  the  mem'bers  of  the  Seminar  that  this 
cause  of  variation  might  be  regarded  as  a  negligible  factor. 


33 

It  will  be  observed  that  with  the  High  School,  A  Grammar 
and  Seventh  Grades  the  interval  and  the  average  of  errors 
is  comparatively  uniform  in  the  first  repetition,  and  that  the 
reduction  of  the  average  of  errors  on  the  part  of  the  high 
school  pupils  furnishes  an  exception  in  the  second.  The  one 
day  interval  caused  reduction  in  the  average  of  errors  of  more 
than  ten  in  each  case.  A  reduction  of  1.3  in  the  average  of 
errors  is  the  least  reduction  that  was  caused  by  the  thirteen 
day  interval ;  but  that  there  was  a  reduction  in  each  case  is 
an  indication  that  this  interval  is  too  short. 

The  twenty-eight  day  interval  caused  a  reduction  with  the 
high  school  and  Seventh  Grade,  B.  Division,  but  a  considerable 
increase  in  A  Grammar.  The  A  Grammar  furnishes  another 
exception  in  that  it  indicates  a  reduction  in  the  average  of 
errors  when  the  interval  is  nearly  twice  as  long.  This  would 
indicate  that  the  increase  of  the  average  in  the  former  repe- 
tition was  probably  due  to  some  disturbing  factor  and  the 
conclusion  could  still  be  drawn  that  an  interval  of  a  month 
is  not  too  long. 

In  the  Seventh  Grade,  A  Division,  the  interval  was  made 
seventy- four  days  and  the  average  of  errors  is  nearly  doubled. 
In  the  Seventh  Grade,  B  Division,  an  interval  of  thirty-nine 
days  and  of  forty  days  caused  a  reduction.  Thirty  day  inter- 
val which  was  fixed  between  the  last  repetition  caused  con- 
siderable reduction  in  each  case  except  with  the  Seventh 
Grade,  B  Division,  where  it  remained  the  same. 

It  will  be  noticed  that  the  reduction  in  each  case  in  the 
last  repetition  is  quite  considerable  except  in  the  case  of  the 
Seventh  Grade,  B  Division,  where  there  is  no  change.  It  will 
also  be  seen  that  there  is  su  reduction  in  every  case  where  the 
interval  was  less  than  fifty  days  except  in  the  forty-nine  day 
interval  with  the  high  school 

Though  it  by  no  means  follows  as  an  undeniable  conclu- 
sion, the  inference  at  least  seems  justifiable,  that  with  a  repe- 
tition interval  of  about  sixty  days,  the  average  of  error  will  re- 
main fairly  constant.  In  consideration  of  the  rapid  decreases  in 
the  last  repetitions,  the  experimenter  feels  free  to  believe  that 
this  interval  could  be  increased  in  arithmetical  ratio,  in  which 
five  days  would  represent  the  common  difference  of  the  vary- 
ing intervals. 

In  the  opinion  of  the  experimenter,  the  inference  and  the 
belief  above  stated  are  confirmed  by  the  results  summarized 
under.  Fifth  Grade  of  1907  and  Facts  of  Experiment  Three, 
even  though  the  twenty-eight  day  interval  would  seem  to  be 
an  exception. 


34 

Results  with  High  School 


^ 

eg 

10 

CO 

CO 

(M 

_ 

6 

> 

0 

i 

> 

0 
z 

6 

Q 

c 

(-1 

0. 
< 

I 

21 

0 

0 

1 

3 

0 

0 

2 

8 

2 

6 

4 

II 

6 

0 

3 

19 

3 

0 

0 

2 

0 

0 

4 

23 

0 

0 

3 

9 

0 

0 

5 

26 

4 

3 

10 

2 

0 

6 

28 

8 

4 

5 

14 

8 

8 

7 

. . 

2 

0 

2 

0 

0 

. . 

8 

31 

16 

5 

7 

7 

3 

3 

9 

21 

6 

2 

I 

I 

. . 

0 

lO 

32 

7 

6 

3 

3 

2 

0 

11 

12 

0 

0 

0 

0 

2 

0 

12 

10 

0 

0 

0 

0 

0 

13 

18 

13. 

. . 

13 

7 

2 

14 

28 

15 

8 

15 

15 

9 

3 

15 

12 

I 

0 

0 

0 

0 

0 

i6 

29 

0 

0 

I 

0 

I 

0 

17 

12 

I 

0 

4 

2 

2 

0 

i8 

22 

. . 

. . 

2 

2 

0 

0 

19 

16 

5 

3 

5 

2 

0 

4 

20 

25 

2 

I 

I 

I 

0 

0 

21 

4 

4 

0 

I 

0 

0 

0 

22 

39 

9 

4 

7 

8 

7 

3 

23 

21 

5 

7 

8 

7 

I 

24 

30 

5 

I 

2 

I 

0 

0 

25 

22 

4 

0 

5 

26 

17 

2 

2 

4 

5 

3 

27 

23 

5 

3 

3 

4 

I 

4 

28 

14 

0 

0 

0 

0 

0 

0 

29 

'2Z 

0 

0 

0 

0 

I 

30 

30 

3 

3 

2 

0 

0 

0 

31 

15 

0 

2 

I 

0 

0 

0 

32 

22 

0 

2 

0 

0 

0 

0 

33 

22 

II 

6 

4 

0 

0 

2 

34 

13 

0 

0 

0 

0 

2 

35 

22 

0 

I 

0 

0 

0 

36 

4 

0 

0 

2 

0 

0 

0 

Z7 

32 

8 

8 

II 

3 

38 

11 

0 

0 

0 

0 

0 

0 

39 

9 

0 

0 

I 

I 

0 

0 

40 

13 

0 

0 

0 

0 

3 

I 

41 

9 

0 

I 

0 

0 

0 

I 

42 

31 

10 

5 

5 

13 

5 

0 

43 

4 

6 

0 

0 

0 

0 

0 

44 

26 

I 

I 

12 

3 

45 

27 

5 

3 

I 

0 

46 

27 

4 

0 

0 

0 

2 

0 

47 

27 

10 

5 

8 

930  172  83  113  145  89  36 


35 
Results  with  A  Grammar 


^ 

rq 

lo 

ro 

ro 

CM 

ro 

6 
Z 

> 

0 

> 
0 
Z 

>' 
0 
z 

c 

03 

tJ 

I 

27 

8 

3 

4 

7 

4 

4 

2 

34 

18 

10 

10 

4 

8 

4 

3 

28 

12 

6 

4 

23 

5 

2 

4 

3 

4 

5 

23 

10 

10 

II 

II 

8 

6 

23 

17 

II 

16 

23 

7 

24 

II 

5 

12 

8 

3 

2 

8 

28 

17 

11 

7 

II 

. . 

3 

9 

31 

18 

16 

16 

7 

13 

lO 

9 

I 

5 

I 

0 

II 

31 

9 

6 

4 

7 

4 

3 

12 

19 

6 

I 

I 

0 

0 

13 

22 

19 

22 

20 

12 

H 

23 

II 

10 

9 

15 

32 

20 

15 

17 

13 

7 

8 

i6 

22 

4 

2 

3 

5 

r? 

20 

16 

13 

14 

9 

9 

2 

i8 

35 

23 

17 

15 

15 

15 

13 

^9 

24 

16 

II 

4 

I 

4 

20 

25 

17 

15 

16 

16 

15 

6 

21 

.  . 

21 

18 

15 

10 

9 

22 

23 

7 

0 

5 

2 

0 

2 

23 

16 

3 

I 

I 

I 

0 

0 

24 

20 

6 

4 

I 

0 

2 

25 

30 

18 

5 

12 

10 

II 

10 

26 

29 

16 

8 

17 

16 

13 

12 

27 

16 

II 

4 

9 

7 

4 

3 

38 

28 

9 

3 

3 

6 

2 

0 

29 

32 

18 

17 

16 

17 

17 

30 

29 

19 

12 

12 

II 

31 

28 

II 

3 

13 

12 

9 

5 

Z^ 

21 

19 

4 

13 

2 

5 

13 

33 

20 

6 

8 

5 

3 

6 

0 

34 

22 

8 

8 

5 

6 

7 

35 

18 

6 

3 

2 

I 

0 

2 

36 

20 

6 

6 

13 

6 

37 

29 

12 

12 

8 

9 

2 

3 

884  391  290  317  294  194  156 


36 
Results  with  Seventh  Grade 
Seventh  Grade-  B  Division         Seventh  Grade-  A  Division 


3 

_ 

CJ 

10 

ro 

OJ 

cq 

r<5 

0. 

0- 

0 

_ 

(N 

JO 

00 

C\J 

d 

> 

0 

>' 
0 
Z 

> 

0 
z 

6 

0) 

Q 

% 

d 
Z 

z 

> 
0 

z 

> 
0 
Z 

cl 

^ 

0. 

< 

I 

30 

16 

12 

II' 

7 

9 

5 

I 

23 

8 

0 

3 

0 

0 

2 

23 

6 

5 

I 

2 

I 

2 

17 

3 

0 

0 

0 

3 

15 

9 

17 

14 

13 

9 

3 

37 

16 

15 

21 

23 

15 

4 

26 

10 

14 

10 

7 

I 

5 

4 

31 

11 

2 

3 

7 

5 

7 

0 

6 

4 

I 

I 

0 

5 

^Z 

10 

0 

3 

. . 

2 

6 

16 

9 

10 

7 

8 

5 

5 

6 

26 

18 

6 

12 

8 

7 

7 

19 

3 

2 

0 

2 

3 

0 

7 

29 

7 

3 

12 

6 

8 

16 

8 

8 

10 

2 

3 

4 

8 

17 

6 

7 

10 

3 

9 

10 

I 

I 

0 

0 

1 

0 

9 

26 

17 

8 

21 

19 

19 

lO 

24 

8 

6 

4 

5 

0 

4 

10 

34 

20 

16 

II 

23 

II 

II 

5 

0 

I 

0 

0 

0 

II 

26 

7 

9 

10 

12 

4 

12 

25 

6 

6 

I 

I 

I 

3 

12 

29 

10 

0 

0 

4 

6 

13 

28 

II 

13 

8 

8 

6 

3 

13 

22 

9 

9 

I 

0 

14 

17 

9 

0 

II 

10 

4 

8 

14 

20 

16 

15 

13 

0 

0 

15 

17 

10 

II 

2 

9 

0 

15 

19 

6 

10 

7 

5 

8 

i6 

24 

7 

5 

3 

4 

4 

3 

16 

31 

18 

14 

26 

22 

18 

17 

36 

14 

15 

7 

4 

16 

9 

17 

20 

7 

0 

3 

0 

0 

18 

19 

4 

5 

4 

3 

3 

. . 

18 

22 

15 

8 

6 

9 

2 

19 

26 

19 

22 

20 

5 

14 

19 

18 

8 

3 

10 

I 

0 

20 

23 

5 

5 

2 

2 

0 

. . 

20 

II 

0 

I 

0 

I 

21 

20 

6 

5 

4 

4 

0 

I 

21 

16 

6 

3 

0 

0 

:i2 

30 

18 

16 

12 

12 

2 

3 

22 

23 

10 

2 

0 

9 

0 

448 

190 

154 

141 

125 

77 

77 

24 

25 

23 
25 
26 

7 
0 
6 

9 
5 
8 

2 

15 
18 

ID 
II 

6 
17 

594  241  127  206  160  144 


37 


p 


2 

i  5 
■s-s  "s 

d  S*  6 

zo;  z 


Xi 
3  go 

o  t^ 


>  C 


46 

44 
41 
44 
44 
43 
41 


High  School 

930  20.2  224  days 

172  3.9    I  day 

83  2.02  13  days 

113  2.5   28  days 

145  3.3   49  days 

89  2.07  30  days 

36  .88  30  days 


A  Grammar 

1  36  884  24.5  227  days 

2  33  391  11-8    I  day 
8.5   13  days 


34  290 

32  317 

36  294 

26  194 

30  156 


9.9  28  days 

8.16  49  days 

7.46  30  days 

5.2  29  days 


Seventh  Grade-  A  Division 

I  25  594  23.7  237  days 


2  24  241 

3  23  127 

4  22  206 

5  22  160 

6  23  144 


10.04  I  day 

5.5  13  days 

9.36  74  days 

7.27  33  days 

6.26  30  days 


Seventh  Grade-  B  Division 
I  21  448  21.3  237  days 


22  190 

21  154 

22  141 
22  125 
20 
20 


77 
77 


8.6  I  day 

7.3  13  days 

6.4  28  days 
5.68  39  days 
3.8  40  days 
3.8  29  days 


Fifth  Grade  of  1907 
Facts  of  First  Experiment 

1  35  416.5  1 1.9  2omos. 

2  35   90-83  2.59  2  days 

3  35   98    2.8  28  days 

4  34   63.3   1.8  30  days 

Results  with  Facts  of 
Experiment  Three 

1  41  397   9-7   9-5  mos. 

2  40  284   6.5   64  days 

3  38  197   5-2   53  days 


DNIVERSITY  OF  CALIFORNIA 


LIBKAEr 


STAIIPED  BELOW 


NOV   SI  1916 
JAN  a  1923 


'''    9  1916 
APR  38  1948 


m  i3 


i'SOHl 


535s 
J53  LU 


DECS     J954LU 


'^^    31981 

•"^'0    WR  3  0  ;9f(i 


30w-l,'15 


